No-take marine protected areas (MPAs) are a commonly applied tool to reduce human fishing impacts on marine and coastal ecosystems. However, conservation outcomes of MPAs for mobile and long-lived predators such as sharks are highly variable. Here, we use empirical animal tracking data from 459 individual sharks and baited remote underwater video surveys undertaken in 36 countries to construct an empirically supported individual-based model that estimates the conservation effectiveness of MPAs for five species of coral reef-associated sharks (Triaenodon obesus, Carcharhinus melanopterus, Carcharhinus amblyrhynchos, Carcharhinus perezi, and Ginglymostoma cirratum). We demonstrate how species-specific individual movement traits can contribute to fishing mortality of sharks found within MPAs as they move outside to adjacent fishing grounds. We discovered that the world’s officially recorded coral reef-based managed areas (with a median width of 9.4 km) would need to be enforced as strict no-take MPAs and up to 5 times larger to expect protection of the majority of individuals of the five investigated reef shark species. The magnitude of this effect depended on local abundances and fishing pressure, with MPAs required to be 1.6–2.6 times larger to protect the same number of Atlantic and Caribbean species, which occur at lower abundances than similar species in the western Pacific. Furthermore, our model was used to quantify partially substantial reductions (>50%) in fishing mortality resulting from small increases in MPA size, allowing us to bridge a critical gap between traditional conservation planning and fisheries management. Overall, our results highlight the challenge of relying on abundance data alone to ensure that estimates of shark conservation impacts of MPAs follow the precautionary approach.